Determining contrast sensitivity functions for monochromatic light emitted by
high-brightness LEDs
Vasudha Ramamurthy, Nadarajah Narendran, Jean Paul Freyssinier, Ramesh Raghavan and Peter
Boyce
Lighting Research Center
Rensselaer Polytechnic Institute, Troy, NY 12180
www.lrc.rpi.edu
Ramamurthy, V., N. Narendran, J.P. Freyssinier, R. Raghavan, and P. Boyce. 2004. Determining contrast
sensitivity functions for monochromatic light emitted by high-brightness LEDs. Third International
Conference on Solid State Lighting, Proceedings of SPIE 5187: 294-300.
Copyright 2004 Society of Photo-Optical Instrumentation Engineers.
This paper was published in the Third International Conference on Solid State Lighting,
Proceedings of SPIE and is made available as an electronic reprint with permission of
SPIE. One print or electronic copy may be made for personal use only. Systematic or multiple
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paper are prohibited.
Determining Contrast Sensitivity Functions
for Monochromatic Light Emitted by High-Brightness LEDs
Vasudha Ramamurthy, Nadarajah Narendran, Jean Paul Freyssinier,
Ramesh Raghavan and Peter Boyce
Lighting Research Center
Rensselaer Polytechnic Institute, Troy, NY 12180
ABSTRACT
Light-emitting diode (LED) technology is becoming the choice for many lighting applications that require
monochromatic light. However, one potential problem with LED-based lighting systems is uneven luminance patterns.
Having a uniform luminance distribution is more important in some applications. One example where LEDs are
becoming a viable alternative and luminance uniformity is an important criterion is backlighted monochromatic
signage. The question is how much uniformity is required for these applications. Presently, there is no accepted metric
that quantifies luminance uniformity. A recent publication proposed a method based on digital image analysis to
quantify beam quality of reflectorized halogen lamps. To be able to employ such a technique to analyze colored beams
generated by LED systems, it is necessary to have contrast sensitivity functions (CSFs) for monochromatic light
produced by LEDs. Several factors including the luminance, visual field size, and spectral power distribution of the
light affect the CSFs. Although CSFs exist for a variety of light sources at visual fields ranging from 2 degrees to 20
degrees, CSFs do not exist for red, green, and blue light produced by high-brightness LEDs at 2-degree and 10-degree
visual fields and at luminances typical for backlighted signage. Therefore, the goal of the study was to develop a family
of CSFs for 2-degree and 10-degree visual fields illuminated by narrow-band LEDs at typical luminances seen in
backlighted signs. The details of the experiment and the results are presented in this manuscript.
Keywords: LED, signage, channel, letter, red, green, blue, backlighted, contrast sensitivity function, uniformity
1. INTRODUCTION
During the past few years, light-emitting diode (LED) technology has been rapidly advancing and has demonstrated
significant benefits over conventional light source technologies in certain lighting applications, such as EXIT signs and
traffic signals. In these applications, LEDs have shown energy savings of more than 80% compared with their
incandescent counterpart. Such large energy savings are realized because colored signs and signals are created using
optical filters over incandescent lamps that absorb and waste a significant portion of the radiant energy generated by the
light source. Alternatively, LEDs are much more efficient in producing monochromatic light. Therefore, LEDs are
becoming the preferred light source for applications that require colored light. However, since LEDs produce much less
light per light source compared with traditional light sources, typically several LEDs are assembled into arrays to meet
the light level requirements of applications. The discrete nature of LEDs could potentially create uneven light
distributions. Additionally, depending on system design, different LEDs in the array could experience different
degradation rates and contribute to the creation of non-uniform luminance patterns over time. Having a uniform
luminance distribution is more important in some applications. One application where LEDs are becoming a viable
alternative and luminance uniformity is an important criterion is backlighted monochromatic signage.1
Backlighted signs have been used outdoors for decades and are an important feature of storefronts that draw customers’
attention, especially during evening hours. Corporations spend a great deal of money to design and manufacture signs
that attract customers, making them an important selling point for a store. Perception of a retail establishment’s quality
may often be based on the illuminated signage in front of that store. For example, a store with certain letters or sections
of its sign burned out may be perceived as lower quality because the sign has not been well-maintained. Similarly, nonuniform luminance distribution within a sign may also affect consumers’ perceptions of the store.
Accepting the fact that LED systems are likely to produce non-uniform luminance patterns, the question becomes: How
uniform should a luminance pattern be? Presently, there is no accepted metric that quantifies luminance uniformity. A
recent publication by Simonson et al. proposed a method based on digital image analysis to quantify the beam quality of
reflector lamps that are commonly used in interior lighting applications.2 In that paper, it is explained that perceived
beam quality depends on several factors including distance of the observer to the target field, background luminance,
target pattern, and target color. In their study, Simonson and others demonstrated that a beam quality rating based on
analyzing a digital image weighted by a contrast sensitivity function (CSF) correlated much better with human subject
ratings, compared with analyzing the raw CCD camera image. To be able to employ such a technique to analyze
colored beams generated by LED systems, it is necessary to have CSFs for monochromatic light produced by LEDs.
1.1 What is CSF?
CSF describes the sensitivity of the visual system as a function of spatial frequencies.3 The size and contrast of a target
come into play when assessing the sensitivity of the visual system. The contrast sensitivity curve (Figure 2) describes
the window of visibility. The curve has points that show the threshold contrast at the respective spatial frequencies.
Beyond these threshold points, an individual may not be able to see a particular spatial frequency. Contrast is derived
from Michelson’s formula, (Lmax–Lmin/Lmax+Lmin), and contrast sensitivity is the reciprocal of contrast. Spatial frequency
is determined by the characteristics of the visual target and is expressed in cycles per degree. The reason for the typical
shape of the curve is that the visual system is less sensitive to very low and very high spatial frequencies. There is an
intermediate point at which the visual system has higher sensitivity than at either extreme. Usually, the CSF falls off
rapidly after reaching a peak of about 3 to 5 cycles per degree.3 With an increase in luminance, the peak value of the
CSF will increase and at the same time, the peak also will shift toward higher spatial frequencies.4 It has also been
shown that there is an effect of field size on the CSF. Carlson showed that the absolute sensitivity to lower spatial
frequencies increases with increasing field size.5 This effect is diminished for higher spatial frequencies, and there is no
significant difference among CSFs.5 Kelly derived CSFs for short, medium, and long wavelength cone photoreceptors
using gratings illuminated with red, green, and blue light sources. During the experimental sessions, subjects were
adapted to an opponent color prior to viewing the test grating. Kelly concluded that under these conditions, there is a
significant difference in the absolute heights and the position of the peaks of CSFs among the short, medium, and long
wavelength cone photoreceptors.6
As mentioned earlier, to develop a metric that can quantify the luminance uniformity of backlighted signs, CSFs are
needed. Although CSFs exist for a variety of light sources at visual fields ranging from 2 degrees to 20 degrees,7 CSFs
do not exist for red, green, and blue light produced by high-brightness LEDs at 2-degree and 10-degree visual fields and
at luminance levels typical for backlighted signage. In reality, a person would look at a backlighted sign on a storefront
within a range of 2-degree to 10-degree visual fields. For example, signage on large-scale department stores would be
seen at about a 2-degree viewing angle when someone is far away from the store, such as driving along a nearby
highway, and at about a 10-degree viewing angle when someone is closer to the store, such as walking toward the store
from the parking lot. Therefore, the goal of the study was to develop a family of CSFs at 2-degree and 10-degree visual
fields illuminated by red, green, and blue LEDs at typical luminances seen in backlighted signs.
2. EXPERIMENT
A human-factors experiment was designed for the purpose of developing a CSF for each of the sine wave grating
patterns illuminated by red, green, and blue LEDs. The experiment comprised two parts: one, to replicate one of the
existing CSFs for white light sources to use as a baseline for comparison, and another to determine the CSFs for
monochromatic light produced by red, green, and blue LEDs. The second part of the experiment was conducted at two
viewing distances corresponding to 2-degree and 10-degree visual field sizes.
2.1 Experimental Setup
The experimental setup (Figure 1) consisted of a 2 ft. x 2 ft. x 9 in. (61 cm x 61 cm x 23 cm) light integrating box built
of 1/4-inch thick white foamboard. The sine wave grating patterns printed on white sheets were mounted at the rear of
the box. These gratings were mounted such that they could be changed easily during the experiment. An array of highbrightness LEDs were mounted on a white foamboard panel that formed the front face of the integrating box. The LEDs
faced the back wall of the box where the gratings were placed. Three separate front panels were built, each one with a
different colored LED array (red, green, and blue). During the experiment, the respective front panel was mounted
depending on the required color. The LED array was wrapped around an 8 in. x 11 in. (20 cm x 28 cm) aperture cut into
the front panel. For the purpose of replicating one CSF for broad-band white light, two 40 W incandescent light sources
were mounted inside the box, one on the left panel and the other on the right panel closer to the front side of the box.
Both the LED and incandescent light sources were powered by a direct current power supply. The average luminance
values of the illuminated gratings were measured before and after each subject’s experiment. The average luminance
[(Lmax+Lmin)/2] is the mean of the darkest and the lightest part of the gratings.
The target sine wave gratings were viewed by the subjects from a distance of 9.5 ft. (2.9 m) for the 2-degree visual field
experiment and at a distance of 1.8 ft. (0.6 m) for the 10-degree visual field experiment. The variables of the sine wave
gratings were their contrast and spatial frequency. The contrast of the grating is defined by (Lmax-Lmin)/(Lmax+Lmin),
where Lmax is the luminance at the peak of the grating, and Lmin is the luminance at the trough. The spatial frequencies
of the gratings chosen were 1, 2, 3, 4, 6, 8, 10, 12, 14, 16, and 32 cycles per degree. These gratings were created using
computer software and were printed on white sheets of paper. In one series of tests, an average target luminance of 45
cd/m2 was maintained for all red, green, and blue target gratings. In a second series of tests, the average target
luminance was based on the typical luminance of red, green, and blue backlighted signs (red: 125 cd/m2, green: 35
cd/m2, blue: 5 cd/m2) determined during a field survey.
2.2 Experiment 1
The objective of the first experiment was to replicate an existing CSF for a broad-band white light source. Seven
subjects, three females and four males in the age group of 20 to 30 years, participated in this experiment. Subjects were
initially tested for color vision deficiencies, and only those with normal color vision participated in the experiments.
During the first experiment, subjects viewed the target sine wave gratings illuminated by the incandescent light sources
from a distance of 9.5 ft. (2.9 m). The visual field for this case was 2 degrees. The experiment was conducted at a
luminance of 45 cd/m2. A two-minute dark adaptation time was given to each subject at the beginning of the
experiment. The target gratings were presented in a random order of contrast for a duration of two seconds for each
spatial frequency. The subjects were asked whether they could see any vertical gratings during each grating
presentation. If they did, that particular contrast value was recorded. The mean contrast value was obtained from the
data for each spatial frequency. The reciprocal of the mean contrast value provided the value for the contrast sensitivity,
which was then plotted against the spatial frequencies to form the CSF.
2.2.1 Results: 2-degree visual field
The result (Figure 2) is compared with the result obtained by Robson8 for a white light source at a luminance of 20
cd/m2 and at a 2.5-degree visual field. Figure 2 shows that the two CSFs are identical at higher spatial frequencies but
deviate slightly in the lower frequency region. This small deviation could be due to the fact that the 2-degree visual
field used in this study is smaller than the 2.5-degree field used in Robson’s experiment, which in turn results in fewer
cycles in the field of view. Past literature shows that at low spatial frequencies, the values of contrast sensitivity
decrease when fewer cycles are presented in the field of view.9 This analysis shows that the apparatus is adequate for
developing CSFs for sine wave gratings illuminated by monochromatic red, green, and blue LEDs.
2.3 Experiment 2
The objective of the second experiment was to develop the CSFs for red, green, and blue light produced by highbrightness LEDs. The peak wavelengths of the red, green, and blue LEDs used in this study are 625 nm, 525 nm, and
475 nm, respectively. The procedure was very similar to Experiment 1. Fourteen subjects, an equal number of males
and females in the age group of 20 to 30 years, participated in Experiment 2. The experiment was initially conducted for
the 2-degree visual field. During this experiment all three colors were kept at an equal luminance, 45 cd/m2. Then the
experiment was repeated at different luminances: 125 cd/m2 for red, 35 cd/m2 for green, and 5 cd/m2 for blue. Finally,
the experiment was repeated for the 10-degree visual field by moving the subjects closer to the experimental apparatus.
2.3.1 Results: 2-degree visual field
Figure 3 shows the CSFs for the different colors, all measured at the same luminance level of 45 cd/m2. The visual field
was 2 degrees. At an equal luminance of 45 cd/m2, the red, green, and blue CSFs overlapped in the higher spatial
frequency region, but they separated out slightly at the lower spatial frequency region. Figure 4 shows the CSFs for
each of the colors at different luminances. The visual field size was once again 2 degrees. As mentioned earlier, these
were the typical luminance levels for the red, green, and blue backlighted signs surveyed. It appears that the peak values
of the CSF increased with increasing luminance levels, and they also shifted to higher spatial frequency values. These
results are consistent with CSFs found in the literature.4
2.3.2 Results: 10-degree visual field
Figures 5 and 6 illustrate the results for the 10-degree visual field at an equal luminance level of 45 cd/m2 and at
different luminance values of 125 cd/m2 for red, 35 cd/m2 for green, and 5 cd/m2 for blue, respectively. In this case, the
CSFs of all three colors overlapped. Neither luminance nor color variation seem to have an impact on the CSFs. For the
10-degree field of view, the peak values of the CSFs occurred at smaller spatial frequencies, 2 to 3 cycles per degree,
compared with 6 to 7 cycles per degree for the 2-degree visual field results. Furthermore, the values of contrast
sensitivity for the 10-degree case were greater at all spatial frequencies compared with the 2-degree case. This is again
consistent with results seen from past studies.5, 7, 10
3. SUMMARY
To be able to employ digital image analysis to quantify the beam quality of colored beams generated by monochromatic
LEDs, it is necessary to have appropriate contrast sensitivity functions (CSFs). Although CSFs exist for a variety of
light sources at visual fields ranging from 2 degrees to 20 degrees, CSFs do not exist for narrow-band red, green, and
blue LEDs at 2-degree and 10-degree visual fields and at luminance levels typical for backlighted signage. Therefore,
an experiment was conducted, and a family of CSFs was derived for 2-degree and 10-degree visual fields illuminated
by narrow-band LEDs at typical luminance levels.
ACKNOWLEDGEMENTS
The authors gratefully acknowledge Jennifer Taylor, Andrew Bierman, John D. Bullough, and Martin Overington of the
Lighting Research Center for their valuable input and help in preparing this manuscript.
REFERENCES
1. Freyssinier, J.P., Zhou, Y., Ramamurthy, V., Bierman, A., Bullough, J.D., Narendran, N., “Evaluation of lightemitting diodes for signage applications,” Third International Conference on Solid State Lighting, Proceedings of
SPIE, Ferguson, I.T., Narendran, N., DenBaars, S.P., Carrano, J.C., editors, Vol. 5187, International Society for
Optical Engineering, San Diego, Calif., Aug. 5-7, 2003 (in press).
2. Simonson, K., Narendran, N., Boyce, P. and Bierman, A. “Development of a metric to quantify beam quality of
reflectorized lamps.” Journal of the Illuminating Engineering Society, 32, no. 1, 63 – 72, 2003.
3. Campbell, F.W. and Robson, J.G., “Application of fourier analysis to the visibility of gratings,” J. Physiol., 197,
551 – 566, 1968.
4. Van Nes, F.L. and Bouman, M.A., “Spatial modulation transfer in the human eye,” Journal of the Optical Society
of America, 57, 401 – 406, 1967.
5. Carlson, C.R., “Sine-wave threshold contrast-sensitivity function: Dependence on display size,” RCA Review, 43,
675 – 683, 1982.
6. Kelly, D.H., “Spatio-temporal frequency characteristics of color-vision mechanisms,” J. Opt Soc Amer 64, no. 7,
983 – 990, 1974.
7. Barten, P.G.J., Contrast Sensitivity of the Human Eye and Its Effects on Image Quality, SPIE—The International
Society for Optical Engineering, Bellingham, WA, 1999.
8. Robson, J.G., “Spatial and temporal contrast-sensitivity functions of the visual system,” J. Opt. Soc. Am. 56(8),
1141 – 1142, 1966.
9. Savoy, R.L. and McCann, J.J., “Visibility of low-spatial-frequency sine-wave targets: Dependence on number of
cycles,” Journal of the Optical Society of America, Vol. 65, no. 3, 343 – 350, 1975.
10. Rovamo, J., Luntinen, O., and Näsänen, R., “Modelling the dependence of contrast sensitivity on grating area and
spatial frequency,” Vision Research, 33, 2773 – 2788, 1993b.
FIGURES
Plan view
White integrating box
Black foamboard
Printed gratings
LEDs
Subject
10-degree position
Subject
2-degree position
1.8 ft (0.6 m)
9.5 ft (2.9 m)
Front view
Printed gratings
Black foamboard
Figure 1: Experimental setup.
1000
Experiment 1
2
Contrast sensitivity
2-degree, 45 cd/m
100
Robson (1966)
2
2.5-degree, 20 cd/m
10
1
0.1
1
10
Spatial frequency (cycles/degree)
100
Figure 2: Baseline comparison between CSFs derived for incandescent light sources.
1000
2
Contrast sensitivity
red (45 cd/m )
2
green (45 cd/m )
100
2
blue (45 cd/m )
10
1
0.1
1
10
Spatial frequency (cycles/degree)
100
Figure 3. Contrast sensitivity functions derived for 2-degree sinusoidal gratings at a luminance of 45 cd/m2
for red (625 nm), green (525 nm), and blue (475 nm) LEDs.
1000
2
Contrast sensitivity
red (125 cd/m )
2
green (35 cd/m )
100
2
blue (5 cd/m )
10
1
0.1
1
10
Spatial frequency (cycles/degree)
100
Figure 4: Contrast sensitivity functions derived for 2-degree sinusoidal gratings at typical luminance values
(red: 125 cd/m2, green: 35 cd/m2, blue: 5 cd/m2) for red (625 nm), green (525 nm), and blue (475 nm) LEDs.
1000
2
Contrast sensitivity
red (45 cd/m )
2
green (45 cd/m )
100
2
blue (45 cd/m )
10
1
0.1
1
10
Spatial frequency (cycles/degree)
100
Figure 5: Contrast sensitivity functions derived for 10-degree sinusoidal gratings at a luminance of 45 cd/m2
for red (625 nm), green (525 nm), and blue (475 nm) LEDs.
1000
2
Contrast sensitivity
red (125 cd/m )
2
green (35 cd/m )
100
2
blue (5 cd/m )
10
1
0.1
1
10
Spatial frequency (cycles/degree)
100
Figure 6: Contrast sensitivity functions derived for 10-degree sinusoidal gratings at typical luminance values
(red: 125 cd/m2, green: 35 cd/m2, blue: 5 cd/m2) for red (625 nm), green (525 nm), and blue (475 nm) LEDs.